The Ancient Greek dialect of Pamphylia shows extensive influence from the nearby Anatolian languages. Evidence from the linguistics of Greek and Anatolian, sociolinguistics, and the historical and archaeological record suggest that this influence is due to Anatolian speakers learning Greek as a second language as adults in such large numbers that aspects of their L2 Greek became fixed as a part of the main Pamphylian dialect. For this linguistic development to occur and persist, Pamphylia must initially have been settled by (...) a small number of Greeks, and remained isolated from the broader Greek-speaking community while prevailing cultural attitudes favored a combined Greek-Anatolian culture. (shrink)

Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape parameter greater than 1, we ensure that the estimated variance (...) will be positive. We suggest a default log-gamma penalty with λ→0, which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero, thus remaining consistent with the data while being nondegenerate. We also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior. Our default method provides better estimates of model parameters and standard errors than the maximum likelihood or the restricted maximum likelihood estimators. The log-gamma family can also be used to convey substantive prior information. In either case-pure penalization or prior information-our recommended procedure gives nondegenerate estimates and in the limit coincides with maximum likelihood as the number of groups increases. © 2013 The Psychometric Society. (shrink)